in Mathematical Reasoning. 333 
qui consiste a fixer les rapports de ses idées pour Jeur appliquer 
les méme judgements s’executera donc autant plus promptement 
qwil nous sera facile de nous rappeler et de remarquer ces 
rapports*.” 
The almost mechanical nature of many of the operations of 
Algebra, which certainly contributes greatly to its power, has been 
strangely misunderstood by some who have even regarded it as 
a defect. When a difficulty is divided into a number of separate 
onest, each individual will in all probability be more easily 
solved than that from which they spring. In many cases several 
of these secondary ones are well known, and methods of over- 
coming them have already been contrived: it is not merely 
useless to re-consider each of these, but it would obviously 
distract the attention from those which are new: something very 
similar to this occurs in Geometry; every proposition that has been 
previously taught is considered as a known truth, and whenever 
it occurs in the course of an investigation, instead of repeating it, 
or even for a moment thinking on its demonstration, it is referred 
to as a known datum. It is this power of separating the difti- 
culties of a question which gives peculiar force to analytical 
investigations, and by which the most complicated expressions 
are reduced to laws and comparative simplicity. One of the most 
elegant illustrations of this opinion I shall at present briefly 
allude to, as a more detailed account of it will be given 
in a subsequent essay. Among the papers left by the late 
Mr. Spence, is one on a method of solving certain equations of 
differences: elimination is the means by which he proposed to 
* Degerando sur les signes, Tom. Il. p. 196. 
t Of so much importance is this maxim, that it has been adopted by Des Cartes as one 
of his principles of philosophizing. “ Diviser chacune des difficultés en autant des parcelles 
qu'il se pourrait et qu'il serait requises pour les resoudre.” Discours de la Methode. 
uU2 
